How do you find the volume of the solid obtained by rotating the region bounded by #y=x# and #y=x^2# about the line #x=-1#?

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↳Redirected from "How do I change #int_0^1int_0^sqrt(1-x^2)int_sqrt(x^2+y^2)^sqrt(2-x^2-y^2)xydzdydx# to cylindrical or spherical coordinates?"

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Answer 1 · 2014-10-25T05:56:51

By Shell Method,

#V=2pi int_0^1(x+1)(x-x^2)dx=2pi int_0^1(x-x^3)dx#

#=2pi[x^2/2-x^4/4]_0^1=2pi(1/2-1/4)=pi/2#

I hope that this was helpful.